Nemato-hydrodynamics of a viscous drop under shear flow

Simulations of nemato-hydrodynamics on the surface of a viscous drop reveal a complex interplay among nematic ordering, activity-driven bulk flows, and interfacial deformations, giving rise to a wide range of self-organized dynamical behaviors (Firouznia and Saintillan, 2025, Physical Review Research). Building on these findings, we examine the influence of externally imposed shear on the nemato-hydrodynamics of a viscous drop. We first analyze how weak shear affects the spatial organization of topological defects in the surface nematic field, focusing on regimes of small deformation at low shear rates. We then quantify how defect dynamics couple with drop deformation and drive cross-stream migration. Our results provide quantitative insight into the physical mechanisms by which a model active drop—or a simple cell with surface activity—may migrate across streamlines in a flowing environment.